Pseudospectra of Linear Operators

The following contains mathematical formulae and symbols that may become distorted in ASCII text format. The advent of ever more powerful computers has brought with it a new way of conceiving some of the fundamental eigenvalue problems of applied mathematics. If a matrix or linear operator "A" is far from normal, its eigenvalues or more generally its spectrum may have little to do with its behavor as measured by quantities such as ||A**N|| or ||exp(tA)||. More may be learned by examining the sets in the complex plane known as the "pseudospectra" of A, defined by level curves of the norm of the resolvent, ||(zI - A)**-1||. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly non-normal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles